Heat the olive oil in a soup pot over medium heat. Add the onion, garlic, sage, 1 teaspoon of the salt and season with pepper, to taste. Cook, covered, stirring occasionally, until soft and fragrant, about 15 minutes. Raise heat to medium-high, add the tomatoes, and cook, stirring with a wooden spoon, until the tomatoes break up and the onions brown slightly, about 7 minutes. Add the squash and the remaining teaspoon salt, and continue to cook, stirring occasionally, until the squash is tender, about 12 minutes. Add the broth, bring to a simmer, and cook, uncovered, until the vegetables tender, about 20 minutes. Set aside to cool slightly.
Working in batches, puree the soup in a blender, or with an immersion blender. Return the soup to the pot and reheat over medium heat. Stir in the vinegar. Serve the soup in warm bowls with a touch of parmesan cheese if desired.
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